Polyelectrolytes segmental mobility

Thus, in dependence on the way of macromolecule conformation change, ratio of life times of salt bonds and correlation time of macromolecule segment rotation, change of local macromolecule units density, under formation of complex polyelectrolyte-SAS segment mobility of macromolecule may be increased, decreased or remains constant. 

Here Vp has been replaced with the pressure difference between the two points is AP, K°, and K are, respectively, the usual conductivity and the complex conductivity of the electrolyte solution in the absence of the particles, (f> is the particle volume fraction, (j)c is the volume fraction of the particle core, Vc is the volume of the particle core, volume fraction of the polyelectrolyte segments, I4 is the total volume of the polyelectrolyte segments coating one particle, and po, are respectively, the mass density of the particle core and that of the electrolyte solution, and ps is the mass density of the polyelectrolyte segment, V is the suspension volume, and p(cai) is the dynamic electrophoretic mobility of the particles. Equation (26.4) is an Onsager relation between CVP and pirn), which takes a similar form for an Onsager relation between sedimentation potential and static electrophoretic mobility (Chapter 24). 

As seen in the preceding section, the counterions play a crucial role in the mobility of the polyelectrolyte molecules. Even in the absence of an external electric field, the counterions exert an induced electric field in the immediate environment of a charged segment which in turn significantly modifies the collective diffusion coefficient of the polymer. This additional contribution is absent for uncharged polymers, where the cooperative diffusion coefficient Dc is given by the Stokes-Einstein law in dilute solutions. 

The origin of the spherical polar coordinate system (r, 9, cp) is held fixed at the center of one particle and the polar axis (9 = 0) is set parallel to E. Let the electrolyte be composed of M ionic mobile species of valence zt and drag coefficient A,-(/ = 1, 2,. . . , M), and let nf be the concentration (number density) of the ith ionic species in the electroneutral solution. We also assume that fixed charges are distributed with a density of pflx. We adopt the model of Debye-Bueche where the polymer segments are regarded as resistance centers distributed in the polyelectrolyte... 

The polarization of a DMA-labeled PMAA sample was monitored [18] as afunction of pH, and rc was later derived [46] at various degrees of ionization, via Equation 2.28. tc varies from ca. 32 ns at a = 0 to ca. 6 ns at a = 0.8. Not surprisingly, the authors [46] offered a similar explanation for the pH dependence of xc to that of Anufrieva and Gotlib [16] essentially, abreakdown in the hypercoil structure occurs as a increases and the polyelectrolyte expands allowing increased mobility of the chain segments. 

For the case where the hxed charges are not uniformly distributed in the polyelectrolyte layer and that the relative permittivity in the poly electrolyte layer does not take the same value as that in the bulk solution phase, the above theory must be modihed as discussed by Ohshima and Kondo [52] and Hsu et al. [54]. Tseng et al. [55] considered the effects of charge regulation on the mobility in the polyelectrolyte layer. The case where the polyelectrolyte layer is not fully ion-penetrable is considered in Ref. [56]. Varoqui [57] considered the case where electrically neutral polymers are adsorbed with an exponential segment density distribution onto the particle surface with a charge density. Ohshima [58] extended Varoqui s theory [57] to the case where adsorbed polymers are charged. Saville [59] and Hill et al. [60] considered the relaxation effects of soft particles in electrophoresis. 

Ohshima, H., Electrophoretic Mobility of a Polyelectrolyte Adsorbed Particle Effect of Segment Density Distribution, J. Colloid Interface Sci., 1997, 185, 269-273. 

Recently, Souza and co-workers have described a special class of hybrid polyelectrolyte in which ion mobility presents an Arrhenius-type behavior above Tg, suggesting a segmental motion decoupled polymer system. Besides, the ion transport mechanism seems to be governed by thermally active ion hopping with the counter-ion fixed in the hybrid matrix. Based on this concept, many possibilities in solid state chenustry and physics arising within the several areas of elecfroactive and optically active... 

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